Taylor Series

The definition of the Taylor Series would not make any sense to you at this point, since it involved calculus operations.

The things I do want you to understand about Taylor Series are as follows:

1. The Taylor Series for a function gives us a series of Taylor polynomials that can be used to approximate the values of the function.

2. Different functions have different Taylor series. Some of the main ones are given on the worksheet.

3. The more terms you use in the Taylor series, the closer the value of the series will be to the actual function.

For example the Taylor series for cos(x) is 1 - x^2 / 2 + x^4 / 24 - x^6 / 720 etc..

If we use just the first two terms, the polynomial will be 1 - x^2 / 2. For x = .1 this gives us the value 1 - .1^2 / 2 = .995. The actual value of cos(.1) is 0.9950041652.

If we use the first three terms the polynomial is 1 - x^2 / 2 + x^4 / 24. For x = 1 this gives us the value 1 - .1^2 / 2 + .1^4 / 24 = .9950041666, must closer to the actual value 0.9950041652, but not exactly equal to it.